Solve the following inequalities: 1/x + 2/(x-1)le 4

Cierra Castillo 2022-07-03 Answered
Solve the following inequalities:
1 x + 2 x 1 4
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Answers (2)

enfeinadag0
Answered 2022-07-04 Author has 16 answers
1 x + 2 x 1 4
1 x + 2 x 1 4 0
1 x ( x 1 ) x 1 + 2 x 1 x x 4 x x x 1 x 1 0
x 1 + 2 x 4 x 2 + 4 x x ( x 1 ) 0
( 1 ) 4 x 2 + 7 x 1 x ( x 1 ) 0 ( 1 )
4 x 2 7 x + 1 x ( x 1 ) 0
4 x 2 7 x + 1 = 0
x = ( 7 ) ± ( 7 ) 4 ( 4 ) ( 1 ) 2 ( 4 )
= 7 ± 33 8
x ( x 1 ) = 0
x = 0 ; x = 1
25 < 33 < 36
5 33 < 6
7 + 33 8 , 7 33 8
x = 1 : 4 ( 1 ) 3 7 ( 1 ) + 1 1 ( 1 1 ) = 12 2 0
x = 0 , 001 0 : 4 ( 0.001 ) 2 7 ( 0.001 ) + 1 0.001 ( 0.001 1 ) = 1 # > 0
x = 0.99 : 4 ( 0.99 ) 2 7 ( 0.99 ) + 1 0.99 ( 0.99 1 ) = 2 # 0
x = 1.001 : 4 ( 1.001 ) 2 7 ( 1.001 ) + 1 1.001 ( 1.001 1 ) = 2 + # < 0
x = 10 : 4 ( 10 ) 2 7 ( 10 ) + 1 10 ( 10 1 ) = + + 0
Solution: ( ; 0 ) [ 7 33 8 ; 1 ) [ 7 + 33 8 ; ]
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Jeffrey Jordon
Answered 2022-07-07 Author has 2581 answers

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